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A223036 Primes p whose smallest positive quadratic nonresidue is a primitive root of p. 2
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 107, 113, 127, 131, 137, 139, 149, 163, 167, 173, 179, 181, 193, 197, 199, 211, 223, 227, 233, 239, 241, 257, 263, 269, 281, 293, 317, 347, 349, 353, 359, 373, 379, 383 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See the complementary sequence A222717 for comments.

LINKS

Table of n, a(n) for n=1..57.

Index entries for primes by primitive root

EXAMPLE

The smallest positive quadratic nonresidue of 3 is 2, and 2 is a primitive root of 3, so 3 is a member.

MATHEMATICA

nn = 100; NR = (Table[p = Prime[n]; First[ Select[ Range[p], JacobiSymbol[#, p] != 1 &]], {n, nn}]); Select[ Prime[ Range[nn]], MultiplicativeOrder[ NR[[PrimePi[#]]], #] == # - 1 &]

CROSSREFS

Cf. A001918, A053760, A222717.

Sequence in context: A172146 A225670 A165255 * A155058 A007703 A002556

Adjacent sequences:  A223033 A223034 A223035 * A223037 A223038 A223039

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Mar 13 2013

STATUS

approved

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Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)